Now showing items 1-20 of 436

    • Chromatic Number of Random Signed Graphs 

      Yuan, Dao Chen (University of Waterloo, 2024-05-03)
      We naturally extend Bollobas's classical method and result about the chromatic number of random graphs chi(G(n,p)) ~ n/log_b(n) (for p constant, b=1/(1-p)) to the chromatic number of random signed graphs to obtain chi(G(n,p,q)) ...
    • Routing, Scheduling, and Sorting in Consolidated Networks 

      Van Dyk, Madison (University of Waterloo, 2024-04-25)
      Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes ...
    • Analytic Methods and Combinatorial Plants 

      Chizewer, Jeremy (University of Waterloo, 2024-04-08)
      Combinatorial structures have broad applications in computer science, from error-correcting codes to matrix multiplication. Many analytic tools have been developed for studying these structures. In this thesis, we examine ...
    • Graph-Theoretic Techniques for Optimizing NISQ Algorithms 

      Jena, Andrew (University of Waterloo, 2024-02-15)
      Entering the NISQ era, the search for useful yet simple quantum algorithms is perhaps of more importance now than it may ever be in the future. In place of quantum walks, the quantum Fourier transform, and asymptotic results ...
    • Formalizing the Excluded Minor Characterization of Binary Matroids in the Lean Theorem Prover 

      Gusakov, Alena (University of Waterloo, 2024-01-23)
      A matroid is a mathematical object that generalizes the notion of linear independence of a set of vectors to an abstract independence of sets, with applications to optimization, linear algebra, graph theory, and algebraic ...
    • Implementing the Castryck-Decru attack on SIDH with general primes 

      Laflamme, Jeanne (University of Waterloo, 2024-01-09)
      With the rapid progress of quantum computers in recent years, efforts have been made to standardize new public-key cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular ...
    • Graphical CSS Code Transformation Using ZX Calculus 

      Li, Sarah Meng (University of Waterloo, 2023-12-21)
      In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps ...
    • Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs 

      Alghasi, Mahtab (University of Waterloo, 2023-12-19)
      Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ...
    • Nonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programming 

      Weames, Tyler (University of Waterloo, 2023-12-19)
      In this thesis, we study the effects of applying a modified Levenberg-Marquardt regularization to a nonsmooth Newton method. We expand this application to exact and inexact nonsmooth Newton methods and apply it to the ...
    • Bipartite Quantum Walks and the Hamiltonian 

      Chen, Qiuting (University of Waterloo, 2023-09-26)
      We study a discrete quantum walk model called bipartite walks via a spectral approach. A bipartite walk is determined by a unitary matrix U, i.e., the transition matrix of the walk. For every transition matrix U, there is ...
    • Uniform Generation of Graphical Realizations of Joint Degree Matrices 

      Zhou, Qianye (University of Waterloo, 2023-09-21)
      In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously employed an MCMC-based method to address this ...
    • Rigidity of near-optimal superdense coding protocols 

      Zhou, Xingyu (University of Waterloo, 2023-09-19)
      Rigidity in quantum information theory refers to the stringent constraints underlying optimal or near-optimal performance in certain quantum tasks. This property plays a crucial role in verifying untrusted quantum devices ...
    • Distance-Biregular Graphs and Orthogonal Polynomials 

      Lato, Sabrina (University of Waterloo, 2023-09-15)
      This thesis is about distance-biregular graphs– when they exist, what algebraic and structural properties they have, and how they arise in extremal problems. We develop a set of necessary conditions for a distance-biregular ...
    • Towards Private Biometric Authentication and Identification 

      Gold, Jonathan (University of Waterloo, 2023-09-05)
      Handwriting and speech are important parts of our everyday lives. Handwriting recognition is the task that allows the recognizing of written text, whether it be letters, words or equations, from given data. When analyzing ...
    • Enumerating matroid extensions 

      Redlin Hume, Shayla (University of Waterloo, 2023-09-01)
      This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ...
    • Cryptography and Privacy in Vehicular Communication Networks 

      Sharma, Pravek (University of Waterloo, 2023-08-28)
      Wireless communication technologies can support dynamic networks between vehicles, pedestrians and roadside infrastructure called Vehicular Ad hoc Networks (VANETs). Wireless communication over VANETs allows for several ...
    • A Linear Algebraic Method on the Chromatic Symmetric Function 

      Haithcock, Evan (University of Waterloo, 2023-08-28)
      The Stanley-Stembridge conjecture is a longstanding conjecture that has evaded proof for nearly 30 years. Concerned with the e-basis expansions of the chromatic symmetric functions of unit-interval graphs, this conjecture ...
    • Chosen Ciphertext Security from Zero Knowledge Proofs 

      Steckel, Camryn (University of Waterloo, 2023-08-24)
      When designing encryption schemes, there are different levels of security that one can achieve. Of the two main security levels, cryptographers generally strive for the stronger notion of chosen ciphertext attack (CCA) ...
    • Solving Saddle Point Formulations of Linear Programs with Frank-Wolfe 

      Hough, Matthew (University of Waterloo, 2023-08-24)
      The problem of solving a linear program (LP) is ubiquitous in industry, yet in recent years the size of linear programming problems has grown and continues to do so. State-of-the-art LP solvers make use of the Simplex ...
    • Algorithmic and Linear Programming-Based Techniques for the Maximum Utility Problem 

      Lawrence, Paul (University of Waterloo, 2023-05-25)
      A common topic of study in the subfield of Operations Research known as Revenue Management is finding optimal prices for a line of products given customer preferences. While there exists a large number of ways to model ...


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